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LONDON - Lucian Freud, a towering and uncompromising figure in the art world for more than 50 years, has died after an illness, his New York-based art dealer said yesterday. He was 88.

Mr. Freud was known for his intense realist portraits, particularly of nudes. In recent years, his paintings commanded staggering prices at auction, including one of an obese nude woman sleeping on a couch that sold in 2008 for $33.6 million.

William R. Acquavella, his dealer, said he would mourn Mr. Freud “as one of the great painters of the twentieth century.’’

“He lived to paint and painted until the day he died, far removed from the noise of the art world,’’ he said.

Mr. Freud did not follow the trends of that world, insisting on using his realist approach even when it was out of favor with critics and collectors. He stubbornly developed his own unique style, eventually winning recognition as one of the world’s greatest painters.

“He certainly is considered one of the most important painters of the 20th and 21st centuries,’’ said Brett Gorvy, deputy chairman of the postwar art department at Christie’s auction house in New York. “He stayed with his figurative approach even when it was extremely unpopular, when abstraction was the leading concept, and, as time moved on, his classic approach has proven to be very important. He fought the system and basically won.’’

He said Mr. Freud remained totally dedicated to his work, overcoming all obstacles and painting long hours every day well into his late 80s in a sustained bid to complete his life’s work before his death.

“He lived and breathed his art,’’ said Gorvy. “For someone who was so successful, he was extraordinarily regulated in his day, with three main sittings a day and some at night. He worked each and every day to this very tough regime. He was very aware of his own mortality, and he knew his time was very, very precious.’’